diff --git a/internal/proxy/passthrough_test.go b/internal/proxy/passthrough_test.go
index c788d1f..8f644bb 100644
--- a/internal/proxy/passthrough_test.go
+++ b/internal/proxy/passthrough_test.go
@@ -246,8 +246,9 @@ func TestUpgradedConnectionOutlastsTheTimeouts(t *testing.T) {
 		t.Fatalf("status %d, want %d", res.StatusCode, http.StatusSwitchingProtocols)
 	}
 
-	// Wait past every timeout, then use the connection.
-	time.Sleep(3 * shortTimeout)
+	// Every timeout started before the upgrade was answered: wait past
+	// them all, then use the connection.
+	time.Sleep(3 * shortTimeout / 2)
 	send(t, conn, "still here\n")
 
 	echoed, err := reader.ReadString('\n')
diff --git a/internal/proxy/proxy_test.go b/internal/proxy/proxy_test.go
index 7b4ebab..c6aefe1 100644
--- a/internal/proxy/proxy_test.go
+++ b/internal/proxy/proxy_test.go
@@ -21,11 +21,15 @@ import (
 
 const (
 	// shortTimeout is what a test sets a timeout to, to see it run out.
-	shortTimeout = 300 * time.Millisecond
+	// It starts before the test has set up its case, such as an upgrade
+	// or the app's buffers filling, so it is as long as the hold-up of the
+	// test process that wantTimedOut allows, waitLimit/2: a shorter one
+	// can run out first on a busy host.
+	shortTimeout = 5 * time.Second
 	// shortTimeoutSetting is shortTimeout as a setting's value.
-	shortTimeoutSetting = "300ms"
+	shortTimeoutSetting = "5s"
 	// longTimeoutSetting is a timeout that does not run out in a test.
-	longTimeoutSetting = "10s"
+	longTimeoutSetting = "1m"
 	// waitLimit bounds how long a test waits for what should happen.
 	waitLimit = 10 * time.Second
 	// pollInterval is how often a test looks for a log line.